Notice that the problem provides the both y coordinates `y_1 = 2` , `y_2 = -6` , one x coordinate, `x=1` , and the distance between the points, `d = 17` , hence, you should sbstitute these values in the formula of distance such that:

`17 = sqrt((x_2 - 1)^2 + (2 + 6)^2)`

`17 = sqrt((x_2 - 1)^2 + 64)`

You need to raise to square both sides such that:

`289 = (x_2 - 1)^2 + 64 =>(x_2 - 1)^2 = 289 - 64`

`(x_2 - 1)^2 = 225 => x_2 - 1 = +-sqrt(225) => x_2 - 1 = +-15`

`x_2 = 15 + 1 => x_2 = 16`

`x_2 = -15 + 1 => x_2 = -14`

Hence, evaluating the x coordinate of the points that follow the given conditions yields `(16,-6)` and `(-14,-6).`